Electromagneto-thermo-mechanical behaviors of conductive circular plate subject to time-dependent magnetic fields

Gao, Yuanwen; Xu, Bibo; Huh, Hoon

doi:10.1007/s00707-009-0196-x

Cited by 9 publications

(4 citation statements)

References 19 publications

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“…An understanding of their vibrational properties is crucial in many contexts, e.g. fluid-structure interaction problems, plate and panel flutter in aeronautics [13], energy harvesting of fluttering flexible plates [18], piezoelectric and laminated plates [15,21], as well as their coupling with electro-magnetic and thermal fields [22]. When the plates are thin, vibration amplitudes can easily attain the same order of magnitude as the thickness.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations

et al. 2013

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Nonlinear vibrations of thin rectangular plates are considered, using the von Kármán equations in order to take into account the effect of geometric nonlinearities. Solutions are derived through an expansion over the linear eigenmodes of the system for both the transverse displacement and the Airy stress function, resulting in a series of coupled oscillators with cubic nonlinearities, where the coupling coefficients are functions of the linear eigenmodes. A general strategy for the calculation of these coefficients is outlined, and the particular case of a simply supported plate with movable edges is thoroughly investigated. To this extent, a numerical method based on a new series expansion is derived to compute the Airy stress function modes, for which an analytical solution is not available. It is shown that this strategy allows the calculation of the nonlinear coupling coefficients with arbitrary precision, and several numerical examples are provided. Symmetry properties are derived to speed up the calculation process and to allow a substantial reduction in memory requirements. Finally, analysis by continuation allows an investigation of the nonlinear dynamics of the first two modes both in the free and forced regimes. Modal interactions through internal resonances are highlighted, and their activation in the forced case is discussed, allowing to compare the nonlinear normal modes (NNMs) of the undamped system with the observable periodic orbits of the forced and damped structure.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations

et al. 2013

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“…Finally, let us mention that some analytical solutions to such coupled problems (even with magnetic fields contribution) are available [5,16], but they are valid for specific domains or components distribution in space, so that it is impossible to provide any general probabilistic methodology on their basis; one may use in those cases the Monte-Carlo simulation only to calculate analytically the statistical parameters for the structural response.…”

Section: Variational Formulation Of the Thermo-piezoelectric Problemmentioning

confidence: 99%

Sensitivity, probabilistic and stochastic analysis of the thermo-piezoelectric phenomena in solids by the stochastic perturbation technique

Kamiński

Corigliano

2011

Meccanica

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The main aim here is to present the application of the generalized stochastic perturbation technique to thermo-piezoelectric analysis of solid continua. The general nth order Taylor series representation for all random input parameters and the state functions is employed to formulate the coupled thermo-electro-elasticity equilibrium equations of the additional order; a determination of any probabilistic moments and characteristics is described; the discretization of the problem in terms of the Stochastic perturbation-based Finite Element Method is also provided. Since this expansion includes the lowest order partial derivatives, the structural sensitivity analysis using direct differentiation is performed at the same time with probabilistic modeling contrasted with the Monte-Carlo simulation results. The probabilistic approach is extended here towards an accounting for the stochastic ageing processes, which appear frequently in aggressive external environments and under dynamic excitation. The two parametric stochastic process with Gaussian initial value and ageing velocity is tested for this purpose. The entire procedure is tested on the example of the thermo-electro-elastic pulsation of the beam modeled analytically using the symbolic software MAPLE, where polynomial approximations, design sensitivities, probabilistic moments and their histories are computed and visualized.

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“…Gao et al (2010) analyzed the behavior of MEE plate by formulating an analytical solution in a transient magnetic field. Lee and Lin (2010) developed a transverse magnetic force model for the interface between the air and ferromagnetic material along with the continuation of magneto-elastic stress throughout the material boundary.…”

Section: Introductionmentioning

confidence: 99%

Influence of coupled fields on free vibration and static behavior of functionally graded magneto-electro-thermo-elastic plate

Mahesh

Sagar

Kattimani

2017

Journal of Intelligent Material Systems and Structures

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In this article, the influence of full coupling between thermal, elastic, magnetic, and electric fields on the natural frequency of functionally graded magneto-electro-thermo-elastic plates has been investigated using finite element methods. The contribution of overall coupling effect as well as individual elastic, piezoelectric, piezomagnetic, and thermal phases toward the stiffness of magneto-electro-thermo-elastic plates is evaluated. A finite element formulation is derived using Hamilton’s principle and coupled constitutive equations of magneto-electro-thermo-elastic material. Based on the first-order shear deformation theory, kinematics relations are established and the corresponding finite element model is developed. Furthermore, the static studies of magneto-electro-elastic plate have been carried out by reducing the fully coupled finite element formulation to partially coupled state. Particular attention has been paid to investigate the influence of thermal fields, electric fields, and magnetic fields on the behavior of magneto-electro-elastic plate. In addition, the effect of pyrocoupling on the magneto-electro-elastic plate has also been studied. Furthermore, the effect of geometrical parameters such as aspect ratio, length-to-thickness ratio, stacking sequence, and boundary conditions is studied in detail. The investigation may contribute significantly in enhancing the performance and applicability of functionally graded magneto-electro-thermo-elastic structures in the field of sensors and actuators.

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Electromagneto-thermo-mechanical behaviors of conductive circular plate subject to time-dependent magnetic fields

Cited by 9 publications

References 19 publications

Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations

Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations

Sensitivity, probabilistic and stochastic analysis of the thermo-piezoelectric phenomena in solids by the stochastic perturbation technique

Influence of coupled fields on free vibration and static behavior of functionally graded magneto-electro-thermo-elastic plate

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